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REDUCTIONISM HAS FAILED. “Zen is holism, carried to its logical extreme. If holism claims that things can only be understood as wholes, not as sums of their parts, Zen goes one further, in maintaining that the world cannot be broken into parts at all. To divide the world into parts is to be deluded, and to miss enlightenment.” https://lnkd.in/dmfn9qW View in LinkedIn

SO ENDS this first of two weekends focused on a fearlessly imaginative essay linking William Blake’s grain of sand not just to the world, but to black holes, relativity and the very fabric of the universe, spacetime. It should be an Exemplar for students in the tradition of Darwin’s excavating earthworms, photonic crystals in beetle wings, and peacock feather Iridescence. Looking is not enough, but observing keenly with a primed mind is how science is built. https://lnkd.in/dusKMKM View in LinkedIn

THE ANALOGY. “On the other hand, for initially unjammed states with θ(0) = 0, but with non-vanishing shear, while the rotation still vanishes, there is still convergence θ(τ ) < 0, corresponding to shear jamming in granular matter, provided, we use the Einstein equation " "Rμν = (8πG/c4)(Tμν−(1/2)gμνT) (where T ≡ gμνTμν) with non-negative energy density Tμνnμnν ≥ 0. The presence of an external stress-energy tensor exacerbates jamming, if the analogy holds.” https://lnkd.in/dusKMKM View in LinkedIn

BLACK HOLE MASS. “For example, according to the calculations of Spera et al, a star of mass ≃90M⊙ will be required to produce a remnant of mass mbh = 30 M⊙ if its metallicity is Z/Z⊙ = −0.5. A more metal poor star (−1.5) will need to be only ≃33M⊙ to produce a 30 M⊙ BBH remnant.” (BBH = binary black hole; M⊙ = unit of stellar mass in suns). https://lnkd.in/d8Jh7TB View in LinkedIn

THE NUMBER LINKAGE. “It is clear that if the shear, twist and Ricci tensor vanish, the geodesic congruence is convergent, i.e., θ(τ) < 0 at every τ for θ(0) < 0. This is the case of spontaneous jamming, and is independent of any assumed symmetries of spacetime, spherical or otherwise.” https://lnkd.in/dusKMKM View in LinkedIn

METALLICITIES. “Important to all of these investigations is the realization that massive black hole formation is suppressed in stellar populations with higher metallicites.” https://lnkd.in/d8Jh7TB View in LinkedIn

FROM SAND TO GEODESICS. “An additional justification of this analogy of jammed states with trapped surfaces may be posited on the basis of the Raychaudhuri equation, for timelike geodesic congruence in the case of granular matter.” https://lnkd.in/dusKMKM View in LinkedIn

NOMENCLATURE. “In astronomy, metallicity is the abundance of elements present in an object that are heavier than hydrogen and helium. Most of the normal physical matter in the Universe is either hydrogen or helium, and astronomers use the word "metals" as a convenient short term for "all elements except hydrogen and helium". (ie: a measure of nucleosynthesis in stars). https://lnkd.in/d8DupZu View in LinkedIn

METHOD. “Using these ingredients, together with the current generation of stellar evolution codes, we can provide a grounded estimate of the global distribution of black holes as a function of black hole mass and galaxy stellar mass. With this as a starting point, we are able to quantify the astrophysical parameters needed to produce the observed BBH merger signals observed.” (BBH = binary black hole). https://lnkd.in/d8Jh7TB View in LinkedIn